Sydney and Melbourne are rivals for the title of Most Bestest City In Australia. We've seen a lot of this rivalry on our travels. Newspaper articles often talk about which is, say, the most cultural of the two, and use odd measurements (e.g. How many people saw Russian Ark in each city).
Sydney is undoubtedly prettier, and the harbour is hard to beat with the brilliant opera house. Melbourne isn't much to look at (referred to as "The Wallflower" in some articles) but many prefer it. I think we're biased towards Sydney, having spent three months working and living there. The weather's not been great while we've been here in Melbourne, so that doesn't help. Today (Saturday) has been great though, and we've spent the morning visiting the lovely Botanical Gardens, where we sat and read the paper. We then treated ourselves to a baked potato lunch in a food court on the south bank of the Yarra river.
We're basing ourselves here for a bit. On Tuesday we're off for a week to Ballarat (gold-mining town) and Halls Gap (nature-walk mountain town, which I hilariously call Helm's Deep), then back to Melbourne. Then we're planning another few days away before returning to Melbourne to start the final leg to Sydney (via Canberra). Because the end is in sight, we're starting to plan New Zealand (where we'll spend two months). Yay!